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Consider lim(x to oo)((x^(3)+x^(2)+x+sin...

Consider `lim_(x to oo)((x^(3)+x^(2)+x+sinx)/(x^(2)+2cosx)-asinx-bx+c)=4`. Now, match the following lists and then choose the correct code.

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The correct Answer is:
`(4)`
`underset(xtooo)lim((x^(3)+x^(2)+x+sinx)/(x^(2)+2cosx)-asinx-bx+c)=4`
`implies" "underset(xtooo)lim((x+1+(1)/(x)+(sinx)/(x^(2)))/(1+(2cosx)/(x^(2)))-asinx-bx+c)=4`
`implies" "underset(xtooo)lim(x+1-asinx-bx+c)=4`
`implies" "underset(xtooo)lim((1-b)x-asinx+1+c)=4`
`implies" "1-b=0,a=0" and "1+c=4`
`implies" "b=1,a=0" and "c=3`
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